The invention is related to the field of electromagnetic propagation resistivity well logging. More specifically, the invention is related to methods for processing phase and amplitude measurements made by an electromagnetic propagation resistivity well logging instrument to determine wellbore diameter.
Well logging techniques known in the art include logging-while-drilling (xe2x80x9cLWDxe2x80x9d). LWD includes attaching a logging instrument disposed in a drill collar to a drilling assembly while a wellbore is being drilled through earth formations. Measurements made by the instrument can be transmitted to the earth""s surface by various forms of telemetry, and/or can be recorded in a storage device in the logging instrument for retrieval and processing after the logging instrument is withdrawn from the wellbore.
One type of well logging instrument adapted for LWD, called an electromagnetic propagation resistivity instrument, is described in U.S. Pat. No. 4,899,112 issued to Clark et al, and in U.S. Pat. No. 4,968,940 issued to Clark et al. This instrument makes measurements of electrical resistivity of the earth formations surrounding the wellbore. Generally speaking, the instrument described in these two patents makes measurements of resistivity by generating an electromagnetic field in the earth formations at a transmitter location on the instrument, and determining the phase and amplitude of the electromagnetic field at two or more receiver locations on the instrument. The change in phase and relative amplitude between the signals detected at the receiver locations corresponds to the electrical resistivity.
As explained in the Clark et al ""112 and ""940 patents, the measurement of phase difference is related to the resistivity at a radially closer distance to the wellbore than is the measurement of relative amplitude. As a result of having more than one radial depth of investigation measurement at each instrument position, it has been shown to be possible to generate a radial resistivity profile of the wellbore and earth formations surrounding the instrument. U.S. Pat. No. 4,964,085 issued to Coope et al, for example, describes a method for determining the caliber (diameter) of the wellbore by processing the phase and amplitude measurements made by an electromagnetic propagation logging instrument.
Another method for generating a radial resistivity profile is described in U.S. Pat. No. 5,900,733 issued to Wu et al. This technique is particularly useful where a plurality of transmitter/receiver spacings are available on a particular logging instrument. Generally speaking, the method described in the Wu et al ""733 patent includes generating an initial model of the earth formations, the model including formation layers each having a selected axial thickness and resistivity. The resistivity may be laterally segregated into two or more zones with respect to distance from the axial center of the logging instrument and wellbore. Based on the initial model, a theoretical response of the logging instrument is calculated. The theoretical response of the instrument is compared to the actual response measured in the wellbore. If the difference between the theoretical and measured responses exceeds a selected threshold, the model is adjusted, and a new theoretical response is calculated. The model adjustment, theoretical response calculation and comparison is continued until the difference falls below the selected threshold. The extant model is determined to be the most likely distribution of resistivity in the vicinity of the wellbore.
Another technique for determining wellbore diameter is described in U.S. Pat. No. 4,916,400 issued to Best et al. This technique uses a measure of the difference in phase between a transmitted electromagnetic wave and a signal detected therefrom propagated through a wellbore and earth formations. The phase difference measure can be quantified by a sum of phase differences (called xe2x80x9cphase sumxe2x80x9d) between the transmitted wave at each of two receivers on the logging instrument, or alternatively can be represented by an average of the phase differences between the transmitted wave and the detected signal at a plurality of receivers. For any predetermined value of resistivity of fluid in the wellbore, the phase sum is correlated to a measurement of difference in phase between the receivers (xe2x80x9cphase shiftxe2x80x9d) to determine both the resistivity of the earth formation surrounding the wellbore and the diameter of the wellbore.
Under certain conditions, however, techniques such as described in the Coope et al ""085 patent and the Wu et al ""733 patent do not result in a unique solution for resistivity profile and wellbore diameter. More than one combination of wellbore diameter and formation resistivity distribution may generate a theoretical instrument response that closely matches the measured instrument response. Further, the method described in the Best et al ""400 patent can produce highly uncertain results under a variety of wellbore conditions, including large wellbore diameters.
What is needed is a technique for determining resistivity profile and wellbore diameter which can resolve cases where different combinations of resistivity profile and wellbore diameter result in the same instrument response.
One aspect of the invention is a method is for determining a diameter of a wellbore using electromagnetic propagation measurements. The method includes inducing an electromagnetic field in the wellbore and in an earth formation surrounding the wellbore from a first location along the wellbore. At a first time, a phase is measured, with respect to the electromagnetic field at the first location, of a signal induced by the electromagnetic field at a second and at a third location axially spaced apart from the first location and axially spaced apart from each other. The measuring is then repeated at a second time. A resistivity of the formation, and the wellbore diameter at the first time and at the second time are determined from the measurements of phase made at the first and at the second times. Any ambiguity in the resistivity is resolved by using resistivity determined from the measurements made at the first time.
In one embodiment, the resistivity and wellbore diameter are determined by calculating a phase difference between the signals detected at the second and at the third locations, and calculating a phase sum between the signals measured at the second and third locations. In another embodiment, the phase sum is substituted by a phase average of the phase measurements made at the second and the third locations.